How to download notes from iCloud to iPhone

I'm trying to download my notes from iCloud and put them onto my old iPhone 4s. My iPhone 5s got smashed, but fortunately my notes, contacts, everything was saved to iCloud.

I CANNOT edit any iCloud settings on my iPhone 5. The motherboard has been smashed. (So please don't even mention my iPhone 5.) However, I can see all my files from my iPhone 5 on the iCloud Web Browser.

I have searched Google, Bing, and scoured completely through Apple's help forums and links. I've found plenty of advertising about how freaking cool iCloud is, and info about uploading data from an iDevice onto iCloud, but NOTHING in regards to retrieving that data and putting it on an iDevice.

Can anyone please give a short, clear and concise answer about how to download notes from iCloud to iPhone? And if it's not possible please just say so.